It is very important to stably transmit data provided from a transmitter so that an only desired the intended receiver may receive the data without tapping by the unintended receiver. In order to stably transmit the data, the most traditional scheme is to use a secret key. However, such a scheme may be very complicated to generate and manage the secret key and may not be suitable in various wireless systems. In recent years, other security transmission schemes are attracting attention. These refer to a physical layer security. The physical layer security is realized using various coding schemes or communication/signal processing theory in a communication system.
When data are securely transmitted from the transmitter to the intended receiver, it may have different meanings. Security of data in cryptography indicates that data transmitted from the transmitter may be decoded with a relatively low calculation amount. Since the unintended receiver requires a calculation amount of a very high level to decode, the data cannot be substantially decoded. This is security based on a calculation amount. When a calculation amount really required in the unintended receiver is very high, a system is sufficiently safe. However, to this end, complex distribution and management of a secret key are performed. This is not easy operation.
According to an information theory, security means a mutual information amount between the transmitter and the unintended receiver. Assuming that n represents a length of a transmission code, Xn represents a code transmitted from the transmitter, Zn represents a code received by the unintended receiver, a complete security is expressed by a following condition.I(Xn;Zn)=0, for all n  [Equation 1]where, I(;) represents a mutual information amount. The complete security is satisfied by only one time pad. To this end, since there is a need for a secret key corresponding to a length of transmission data, it is impossible to satisfy the complete security in most cases. A security at a level lower than the complete security is an information theoretic security in strong sense and is defined as follows.
                                          lim                          n              ->              ∞                                ⁢                                          ⁢                      I            ⁡                          (                                                X                  n                                ;                                  Z                  n                                            )                                      =        0                            [                  Equation          ⁢                                          ⁢          2                ]            
Security at the lower level is information theoretic security in weak sense and is defined as follows.
                                          lim                          n              ->              ∞                                ⁢                                          ⁢                                    1              n                        ⁢                          I              ⁡                              (                                                      X                    n                                    ;                                      Z                    n                                                  )                                                    =        0                            [                  Equation          ⁢                                          ⁢          3                ]            
The information theoretic security in strong sense and the information theoretic security in weak sense has a limitation to obtain security when a length of a code is infinitely long. In real application, the length n of the code is finite, and the length of the code is limited due to a transmission delay and complex problem. In particular, the information theoretic security in weak sense has a problem that a real information output amount may be increased if the length of the code is increased. For example, if I(Xn; Zn)=√{square root over (n)}, the information theoretic security in weak sense is satisfied. That is,
            lim              n        ->        ∞              ⁢                  1        n            ⁢              I        ⁡                  (                                    X              n                        ;                          Z              n                                )                      =                    lim                  n          ->          ∞                    ⁢                        1          n                ⁢                  n                      =    0.  However, in this case, if the length of the code is increased, the information output amount is increased. That is, limn→∞I(Xn; Zn)=limn→∞√{square root over (n)}=∞. Up to now, most researches is limited to the information theoretic security in weak sense. The result is applicable to an only relatively simple channel.
Other type of security includes security in a block error probability aspect. When a data transmission rate in the transmitter is less than a channel capacity between the transmitter and the intended receiver and greater than a channel capacity between the transmitter and the unintended receiver, if a length of the code is extremely great (n→∞), a block error probability in the intended receiver converges to zero, and a block error probability in the unintended receiver converges to 1. When the length of the code is finite, a block error probability in the intended receiver does not converge to zero, and a block error probability in the unintended receiver does not exactly converge to 1. However, using random coding exponent and strong converse of Gallager, a block error probability in the intended receiver may be limited to about 0 or less, and a block error probability in the unintended receiver may be limited to about 1 or greater. However, in this manner, security based on the block error probability is not actually and sufficiently safe. For example, consider a case where the length of the code is very long and one bit error occurs among a plurality of bits in a code block. The block error probability is always 1 but the bit error probability is about zero. That is, remaining (n−1) bits except for one among n bits may be exactly decoded by the unintended receiver.
The present invention has been made in an effort to solve the above-described problems associated with prior art, and is aimed at setting a block error probability in the intended receiver to about zero and setting a bit error probability in the unintended receiver to about 0.5 when a length n of a code is finite.